关于无理数的一个性质(英文)

A Property on Irrational Number

假设ｚ是一个无理数。［０，１］区间被｛ｚ｝，｛２ｚ｝，…，｛ｎｚ｝分割成ｎ＋１个区间。该文将证明这ｎ＋１个区间的长度最多只有三个值。如果有三个值，那么最大的一个值等于另二个值的和。

Suppose that z is an irrational number. It will be proved that interval is divided by {z}, {2z},…,{nz} into n+1 intervals, the lengths of these n+1 intervals have at most three values, and if there are three values, the biggest one is equal to the sum of the other two.